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math.SP2023
Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces
Cyril Letrouit, Simon Machado
In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a t…
math.GR2023
The structure of approximate lattices in linear groups
Simon Machado
Approximate lattices are aperiodic generalisations of lattices of locally compact groups that were first studied in seminal work of Yves Meyer. They are defined as those uniformly…
math.GR2023
Small doubling for discrete subsets of non-commutative groups and a theorem of Lagarias
Simon Machado
Approximate lattices of Euclidean spaces, also known as Meyer sets, are aperiodic subsets with fascinating properties. In general, approximate lattices are defined as approximate s…